Yes this is a common confusion among "high schoolers" and not only and initially seems as a paradox from our everyday experience with relative moving objects. The problem goes away if you understand that light is not an object but a wave.
To answer with a paradigm as simply as I can, lets consider the following question and scenario which covers what you actually ask:
In what scenario can you subtract the speeds of a moving light source towards an opposite moving observer towards the light?
According to special relativity c(fixed)=λf=λ/Τ where c is the propagation fixed speed of light in vacuum space, λ the wavelength of light (i.e. distance between two waves) and f the frequency of light (i.e. how many waves per second, color for visible light) with f=1/T where T is the period of time between two light waves, there is no relative speed of light for an observer and the propagation speed of light is absolute, meaning has the same value approximately 3E8 m/s for all observers independent their velocity (i.e. speed and relative direction to a light source).
So No. You cannot add the two velocities and say for example light speed is c=300,000 Km/s and I’m moving towards it with v=20Km/s therefore the relative speed of light is 300,020 Km/s!! NO THAT’S WRONG!!
That what is changing however in the above scenario also deduced from the above formula is, that as you move with a finite speed v towards the light waves you get (T-t) which is equivalent with you seeing shorter wavelength of light thus higher frequency of light. Therefore in the above formula in order to keep c speed always at a fixed value of 3E8m/s the speed of light, if the f=1/(T-t) value goes up because your travelling with a speed v inside the light wave and towards the light source (see figure) then λ value in the equation must go proportionally down so that c speed of light has always the same fixed speed thus 3E8=300,000 Km/s.
So what you would experience would be a Doppler light shift in the frequency of light you see thus a color change. Moving towards the light and you will see the light blue shifted. Moving away from the light and you will see it red shifted.
Nevertheless, there is a loophole on the above arguments which I believe is related to your question and will resolve all your confusion. That in order the above to be true we assume that the light from the light source has already reached you and you can see all this time the light? Thus, you are inside the light waves all this time you are moving. That is the tricky part I believe you are asking and the source of the confusion.
So, is there a scenario where you are allowed to do c-v or c+v for calculating a relative propagation speed of light according to your motion? Yes of course. You are allowed to do that only in the case you have NOT seen yet the light from a light source which was turned on because its light has not reached you yet but it is on its way towards you moving then you are allowed to do any algebraic addition or subtraction depending your relative velocity to calculate the time needed for the light to reach your position in space!! Thus in case you are speeding up towards the coming light is effectively increasing the speed of light you can say to c+v in a vacuum with v being your speed. But if you are already inside the light waves, the speed of light independent of your frame of reference and velocity is always at c=300,000 Km/s. In that case the only thing your motion affects the light is its color thus its frequency.